How to fix bright pixels around light sources?
Those are called fireflies, and there are several easy ways to get rid of them. Fireflies are often present in low-light renders. The following are the three easiest.

Clamping

This is probably easiest and best way to combat fireflies. Turn the Properties panel > Render tab > Sampling drop down > Clamp Indirect: value to 3.



Filter Glossy

Turn the Properties panel > Render tab > Light Paths drop down > Filter Glossy: value to 0.5. This blurs all reflective/refractive elements just a bit.



Samples

Sometimes you just need more samples.

All ideas and images from here.